Problem: Simplify the following expression: $k = \dfrac{4ab + b}{2b^2} + \dfrac{5b^2 + 5ab}{2b^2}$ You can assume $a,b,c \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{4ab + b + 5b^2 + 5ab}{2b^2}$ $k = \dfrac{9ab + b + 5b^2}{2b^2}$ The numerator and denominator have a common factor of $b$, so we can simplify $k = \dfrac{9a + 1 + 5b}{2b}$